Conditional Lie-Bäcklund symmetry reductions and exact solutions of a class of reaction-diffusion equations (Q1629195)

Summary: The method of conditional Lie-Bäcklund symmetry is applied to solve a class of reaction-diffusion equations \(u_t + u_{x x} + Q(x) u_x^2 + P(x) u + R(x) = 0\), which have wide range of applications in physics, engineering, chemistry, biology, and financial mathematics theory. The resulting equations are either solved exactly or reduced to some finite-dimensional dynamical systems. The exact solutions obtained in concrete examples possess the extended forms of the separation of variables.